There's a helpful article written by Georgi Gladyshev in Entropy that addresses appropriate ways of thinking about entropy in evolution. You can find it at http://www.mdpi.org/entropy/papers/e1040055.pdf and I attach it for convenience

I'm afraid the article was over my head. I sent an email to Professors Granville Sewell and Andy McIntosh with the Gladyshev article asking for help. Sewell and McIntosh wrote the articles I attached on June 5.

If that's over your head, you should not be asking a journal to retract a paper on the basis of thermodynamics. As you admitted in a pervious post, your understanding of thermodynamics is limited to a gas in a box. The theromdynamic concepts, however, do apply to liquids, gels, solids and ensembles of those objects and you may be interested in learning how it does.

I appreciate your references to the papers by Sewell and McIntosh but I find neither paper persuasive. Those papers, take us in a very different direction from your assertions. They are focused on a discussion of the mechanisms of entropy change, if I may state it in those terms. You took the approach that thermodynamic parameters are not valid for biological systems, an assertion not supported by anyone, as far as I know.

I think I understand the Gladyshev article well enough to realize that it supports the Styer article in only one respect. He states on page 57,

On the whole, one may assert that both internal factors (characteristics of the biosystem) and external factors (characteristics of the environment) determine the trend of biological evolution, whose progress is, of course, possible thanks to the inflow of solar energy and energy from other sources.

This is what Styer is implying: Heat flows into and out of of Earth is what caused the biosphere to become more complex. This is absurd for two reasons: 1) We don’t know what caused the biosphere to increase in complexity during evolution. 2) Natural selection only explains how species adapt to the environment, not how mammals evolved from bacteria in 3 billion years.

Creationism is irrational, but the idea that the sun caused evolution is downright stupid.

The article does not support the absurd equation in Styer for the entropy of the biosphere: S = 9.53 X 10 (-23) J/K (4c). What is absurd is not the estimate of the probabilities, but the use of the Boltzmann constant, instead of 1 J/K, to calculate the entropy. The Gladyshev article doesn’t say anything about the Gibbs function for an organism. It speaks only about subsystems within an organism. In an earlier article ("On the Thermodynamics of Biological Evolution”, J. theor. Biol. (1978) 75, 425-441), Gladyshev has the equation G = sum of G(i). A biological system contains chemical reactions and if you have enough subsystems you can meaningfully talk about the Gibbs function of those subsystems, I suppose. But nowhere in the article does Gladyshev use the Boltzmann constant to calculate the Gibbs function or the entropy of a subsystem or the organism as a whole.

Keep studying the article until you understand all of it. It's good. Note especially the distinction he emphasizes between kinetics and thermodynamics. This is something that Sewell misses as well. Styer is not talking about kinetics and saying anything like what you are attributing to him. He is talking thermodynamics and showing that total entropy is increasing. That is, while the entropy may be decreasing ever so slightly with evolution, properly taking the entire system into account with the energy flow, the overal entropy still increases and the second law is not violated. That is a result independent of the kinetics of what drives the evolution.

Yes, yes, yes, Boltzmann's constant is involved in relating the density of states to the entropy which is in the Gibb's function which is in Gladyshev's article. If you still cannot understand how temperature and entropy apply not only to gases but also to solids and liquids, then we'll just have to stap this conversation. I've repeated it often enough and explained it thoroughly. Maybe one more hint since you seem to think only in terms of gases contained in a box. Perhaps you might think of each atom in a solid body, or a liquid systems, or the like, as being in a box by itself where the box is formed by the neighboring atoms in a nearly fixed fashion. Yes, it all has a temperature and its entropy is calculated through Boltzmann's constant.

I agree that there is no point in discussing thermodynamics any further. As I said to the editor of the American Journal of Physics, it should be possible for two PhDs in physics to come to an understanding of what the second law of thermodynamics means, but apparently not. This is good news for scientists who suffer from physics envy.

That leaves open only the question of whether natural selection explains the complexity of life. The only theory that explains the complexity of life is the theory of intelligent design, but atheists don’t like to admit this. What is wrong with the theory of intelligent design is that there is no evidence for it. There is no evidence that living organisms are "irreducibly complex.” ID is just a bright idea.

The following quote is from a PhD in linguistics, not biology. Pinker is Steven Pinker who has a PhD in linguistics and Bloom is Paul Bloom who has a PhD in psychology. What we have in this quote is three laymen disagreeing with the expert, Charles Darwin:

They [Pinker and Bloom] particularly emphasized that language is incredibly complex, as Chomsky had been saying for decades. Indeed, it was the enormous complexity of language that made is hard to imagine not merely how it had evolved but that it had evolved at all.

But, continued Pinker and Bloom, complexity is not a problem for evolution. Consider the eye. The little organ is composed of many specialized parts, each delicately calibrated to perform its role in conjunction with the others. It includes the cornea,…Even Darwin said that it was hard to image how the eye could have evolved.

And yet, he explained, it did evolve, and the only possible way is through natural selection—the inestimable back-and-forth of random genetic mutation with small effects…Over the eons, those small changes accreted and eventually resulted in the eye as we know it. (Christine Kenneally, The First Word: The Search for the Origins of Language, pp. 59–60)

Perhaps an analogy will help illustrate why your critique of Styer misses the mark. Suppose Alice and Bob are discussing an ice maker.

Bob: When ice freezes, the entropy decreases. Therefore it violates the second law of theromdynamics.

Alice: No, it doesn't! The ice maker works by plugging it into the electrical outlet and the power from the electric power source provides more entropy than the water/ice system loses, so the second law of thermodynamics is preserved.

Bob: FOUL! You just said that energy from the electric power source causes a decrease in entropy of the ice which is absurd.

Alice: Of course not! The electrical power runs the motor which runs the compressor which transfers the heat from the water to the environment.

In that analogy, Bob made exactly the same mistake you've made. Styer's argument is just like Alice's--looking at the thermodynamics of the entire system, not needing to comment on the kinetics of the compressor and pump that transfer the entropy from the water to the environment. Similarly, Styer didn't need to deal with the kinetics of how the entropy is transferred, only that the total entropy flow is consistent with the second law. Gladysheve rightly articulates the distinction between theromdynamics and kinetics.

I don’t understand why the decrease in the entropy of a system has to be accompanied by a greater increase in the entropy of the environment. When hydrogen atoms come together under the force of gravity to form a star, the entropy of the hydrogen gas decreases without any increase in the entropy of the environment.

The way I understand the idea of Styer and Gladyshev about entropy and evolution is this. There is a sense in which evolution does violate the second law of thermodynamics rooted in the lack of understanding of what caused the complexity of life to increase. Fighting creationists and advocates of intelligent design, atheists cry out in a panic: "The second law about complexity always decreasing only applies to a closed system. The earth is not a closed system because of the sun. The second law of thermodynamics is not violated.”

The entropy of a star does increase. It heats up, doesn't it? The second law does state the entropy will increase in a closed system and indeed that has never been violated to our knowledge.

Your characterization of anyone (and it's not just atheists but also Christians who understand science) responding in panic is rather far off the mark. The response is usually one of exasperation towards people who ought to know better but keep insisting wrongly that evolution violates the second law of thermodynamics. It doesn't at any level of the hierarchy, as Gladyshev rightly points out. In every case, those who argue that evolution violates the second law have in some way misunderstood or misstated thermodynamic principles.

You in particular failed to see that the basic concepts of temperature and entropy apply to more than gases but also to solids and liquids and biological systems. And you wrongly accused Styer of claiming the sun's heat was a mechanistic cause of the reduction of entropy in evolution.

I don’t think hydrogen atoms spread far apart in outer space is a gas. You can calculate the averages kinetic energy of each atom, but to convert the KE to a temperature with the Boltzmann constant doesn’t make sense to me because you can’t measure the temperature of such a rarefied gas with a thermometer.

As the gas atoms come closer together, the volume occupied by the atoms decreases. I suppose there comes a point in the evolution of a star when it becomes meaningful to say it has a temperature. However, long before that point, the complexity of the system has decreased because there is more knowledge about the location of the gas atoms. Likewise, the increase in the complexity of life during evolution does not violate the second law of thermodynamics. It does not violate the second law because the second law is absolutely true. Creationists show bad judgment on this point. The idea that evolution does not violate the second law because the earth is not a closed system strikes me as being absurd.

We should get off the topic of thermodynamics and focus on the question of whether natural selection acting upon innovations explains the complexity of life. Thermodynamics is getting us nowhere. By discussing evolutionary biology, we can get the input of biologists who should understand the limits of natural selection.